Extraction of Sodium Picrate by 3 m-Crown-m Ethers and Their Monobenzo Derivatives ( m = 5 , 6 ) into Benzene : Estimation of Their Equilibrium-Potential Differences at the Less-Polar Diluent / Water Interface by an Extraction Method

and Kex± = [NaL + ]o[Pic − ]o/([Na + ][L]o[Pic − ]), respectively. Here, the subscript “o” denotes an organic (o) phase and practically o = Bz. 15-Crown-5 ether (15C5), 18-crown-6 one (18C6), and their monobenzo (B) derivatives (B15C5 and B18C6) were selected as L. Interfacial equilibrium-potential differences (Δφeq) at extraction were estimated at 298K. A plot of logKex± versus −Δφeq for the four L extraction systems gave a straight line with slope = 84V. This slope was compared with those, reported before, of the dichloromethane (DCM), 1,2-dichloroethane (DCE), and nitrobenzene (NB) extraction systems. The slopes of the regression lines were in the order NB < DCM ≤ DCE < Bz. Also, the individual distribution constants of the complex ion NaL and an ion-pair complex (NaLPic) into Bz phase were calculated from the above extraction data. At least, a comparison between these values suggests that Bz molecules mainly interact with NaL moiety of NaLPic.


Introduction
A presence of interfacial equilibrium-potential differences (Δ eq ) at extraction processes with polar diluents, such as dichloromethane (DCM), 1,2-dichloroethene (DCE), and nitrobenzene (NB), has been clarified [1,2].For example, crown compounds (L) extract silver picrate into DCE [1,2] or alkaline-earth metal (Ca-Ba) picrates [1] into NB.In these studies [1,2], an individual distribution constant ( D,A ) of a pairing anion (A − ), such as picrate ion (Pic − ), has been determined in the course of  ex determination.Here,  D,A and  ex have been defined as  , respectively; the symbols MLA  , M + and the subscript "o" denote an ion-pair complex, a metal ion with the formal charge  (= 1, 2), and an organic (o) phase, respectively.The Δ eq values have been determined by using the experimental  D,A values and the electrochemical equation of log  D,A = −(/2.303)(Δeq − Δ A 0 ) [1], where Δ A 0 refers to a standard formal potential for an A − transfer across the o/water (w) interface and , , and  have usual meanings.Thus the presence of Δ eq at the polar diluent/w interfaces has been examined and proved experimentally [1,2].Also, Δ eq presence had been already described in the distribution study of protonated amino acids into NB [3].However, the presence of Δ eq has not been clearly considered for the extraction of simple salts into NB [4], that of metal salts by extractants, such as calix [4]arene and dibenzo-24-crown-8 ether derivative, into NB [5] or DCE [6], and that of R 4 N + A − into DCE [7] in the field of extraction chemistry and for electrochemical extraction studies [8][9][10] at the liquid/liquid interfaces.Besides, the presence of Δ eq at less-polar diluent/w interfaces has not been clarified so far.Its cause seems to be the lower concentrations of ions present in the less-polar diluents, compared with their concentrations in the polar diluents.Additionally, the correlation between the extraction chemistry and the electrochemistry at the liquid/liquid interfaces had not been reported, except for our studies [1][2][3] and a description [11] with respect to the distribution of a simple salt, such as Bu 4 NBr.
In the present paper, selecting benzene (Bz) as the representative less-polar diluent, we determined from available extraction data [12][13][14][15] Δ eq values at the Bz/w interface.Also, the thus-determined values at 25 ∘ C were compared with Δ eq ones for the DCM, DCE, and NB extraction systems.For the comparison, 15-crown-5 ether (15C5), 18-crown-6 one (18C6), benzo-15C5 (B15C5), and B18C6 were selected as L and NaPic was done as an extract.Moreover, individual distribution constants of the ion-pair complexes NaL + Pic − and the complex ions (NaL + ), which constitute parts of the complexes, into the four diluents were estimated from the above results and then their properties for solute-solvent interaction were discussed.

Redetermination of Compositions of the Ion-Pair
Complexes Extracted into Bz.Plots [16] for redetermining a Na(I) : L : Pic(−I) composition in the four extraction systems yielded regression lines of a slope = 0.99 7 and an intercept = 3.89 (≈log  ex at  = 1) at a correlation coefficient () = 0.998 for the 15C5 system, of 0.99 9 and 3.17 at  = 0.999 9 for the B15C5 one, of 0.90 3 and 3.04 at  = 0.996 for the 18C6 one, and of 1.02 and 3.09 at  = 0.999 for the B18C6 one; see log(/[Pic − ]) versus log[L] Bz plots in Figure 1, where  denotes a distribution ratio of species with Na(I) into the Bz phase.

Determination of Extraction Constants and Their Several
Component Equilibrium Constants.The  D,A and  ex values at A = Pic(−I) and  = 1 were determined by the plot of log where  ex mix has been defined as . Also,  ex± values were determined by the plot of log  ex mix versus −(1/2) log  (Figure 3) based on the equation where the symbol  ex± has been defined as The thus-determined values at 25 ∘ C are listed in Table 1 (see Appendix A for reference), together with their component equilibrium constants,  D,Pic ,  D,NaL (= [1,2,16]). ex values were in the order B18C6 < B15C5 < 18C6 < 15C5, although the ionic strength () for the water phase of the 15C5 system is somewhat smaller than those of the other systems.This order was in accord with those [12][13][14][15] reported before (Table 1) and reflected the order of the (intercept/slope) values for the plots of log(/[Pic − ]) versus log[L] Bz (see Section 3.1).Similarly,  ex± values showed the order B18C6 ≤ B15C5 < 18C6 ≤ 15C5, although the values of the benzo derivatives have large errors.This order agreed with that of  ex .These facts indicate that the present analyses are essentially valid.

On Δ𝜙 𝑒𝑞 Estimation and Its
Correlation with log  ± .We can formally calculate the Δ eq values from the relation [1, 2, 21] (see Table 1), when Δ A 0 values are available.Fyles had evaluated the free energy of the Pic − transfer from w to Bz [22]; then, Δ Pic 0 value at the Bz/w interface was estimated from its free energy to be −0.486V at 25 ∘ C. The thusestimated Δ eq values are listed in Table 1.Δ eq values were in the order 15C5 ≈ 18C6 < B15C5 ≈ B18C6, although their experimental errors were large.Also, one can see that Δ eq values for the Bz system with L are negative, indicating that As Figure 4 shows, a plot of log  ex± versus −Δ eq yielded the straight line: log  ex± = (84 ± 12)(−Δ eq ) − (23.6 ± 2. 6 ) at  = 0.981.Similar lines were observed in NaPic extraction by L into DCM and DCE.Adding the data of NB systems, these slope values at Δ eq (not −Δ eq ) were in the order Bz (slope = −84 V −1 ) < DCE (−26) ≤ DCM (−21) < NB (3).This order was close to that of dielectric constants (  ) [23] of the pure diluents at 298.15 K: Bz (  = 2.27) < DCM (8.93) < DCE (10.23) < NB (34.82), although these diluents were saturated with water.These results can be explained in terms of a model like a parallel-plate capacitor at the diluent/w interface [24].Namely, its capacitance () is expressed as the following equation [24]: Here, the symbols , , , and  refer to a charge stored on the capacitor, a potential across the capacitor, an area of the plate, and an interplate spacing, respectively [24].So assuming that the slopes in V −1 of log  ex± versus −Δ eq plots correspond to  terms, then their values have to be proportional to   ones under the condition of a fixed / in (4).The symbol  can be considered to be the area of the o/w interface and  value corresponding to its area in test tubes which had been used for the extraction experiments into the four diluents was estimated to be 2.4 cm 2 from their mean inner diameter (=1.75 0 cm).A plot of slope versus   showed a positive correlation.From this fact, as an example, it can be considered that  value for Bz is smaller than those for others.Unfortunately, we have no experimental ground with respect to this consideration.[21] and PbPic 2 [25] with 18C6 into various diluents containing Bz.Such a similarity also suggests that the present analysis is valid.

On Some
log  1,Bz values were in the order L = 18C6 ≤ 15C5 < B15C5 < B18C6 (Table 1).This order is close to 18C6 < 15C5, B18C6 < B15C5, which was predicted from a combined parameter,  +   +, of basicity of the donor O atoms (parameter: ), selectivity of L against Na + (  ) with a molecular volume (); see Table 3 and Appendix B for the parameters.Also, an addition of a benzo group to the ring skeletons is causing an increase in  1,Bz : 15C5 < B15C5 and 18C6 < B18C6.That is, its addition which spontaneously changes the parameters , , and  of L (see Table 3 and Appendix B for ) has a positive effect on  1,Bz .
1,Bz value at L = 15C5 was larger than  1,DCE ,  1,DCM , and  1,NB ones;  1,DCM = 10 6.2 M −1 at average  DCM = 3.0 × 10 −6 M,  1,DCE = 10 6.5 at 1.7 × 10 −6 , and  1,NB = 10 5.3 at 3.1 × 10 −6 .Also, the same is true for  1,org values for the other L.These facts indicate that although NaL + Pic − in Bz phases are less dissociable than those in DCM, DCE, and NB phases, the ions are present even in Bz phases.In other words, it suggests that the occurrence of Δ eq is possible at Bz/w interface.The values are a logarithmic individual distribution-constant of a single Na(I) ion into the DCM, DCE, or NB phase and are standardized at Δ eq = 0 V. i See [20] and footnote h.

On the Distribution of 𝑁𝑎𝐿
) of L into the o phase and a complex formation one (=[ML + ]/[M + ][L]) of M + with L in water, respectively.
Comparing Bz system with NB one at L = 15C5, for example, a difference between log  ex±,Bz and log  ex±,NB was −5.2 7 {= log( ex±,Bz / ex±,NB ) = −3.9 1 − 1. S between these diluents greatly contributes the positive difference (=2.8) in log  D,NaL S between them.Also, the same is true for other L's systems with Bz.The same explanation holds in comparison with DCM or DCE system because log  D,Pic S values have been reported to be −1.01 1 [20] for DCE and −0.68 [23] for DCM.In other words, accuracy of  D,Pic S value for Bz system can become important for the discussion of the above larger  D,NaL S values; Fyles had estimated log  D,NaL S value for DCM at −0.44 [22], compared to −0.68 [23].
On the other hand, the orders of the actual  D,NaL values, the values at Δ eq ̸ = 0, were Bz < DCM < DCE < NB for L = 18C6 and Bz < DCE < DCM < NB for the other three (Table 2).Also, the log  D,NaLPic (=log  D,NaLPic S in practice [1]) orders were Bz < DCE < DCM < NB for all the Ls employed.Here, the thermodynamic relation log  D,MLA = log  ex +log( D,L / ML )−log  1 , was used for the calculation [12][13][14][15][16] and the symbol  1 denotes the ion-pair formation constant in M −1 for ML + A − in water.The orders of  D,NaLPic determined in the benzo derivatives systems were in agreement with the corresponding orders [13,15] reported before.This agreement shows a validity of such  D,NaLPic evaluations.For 15C5 and 18C6 systems, log  D,NaLPic values were not cited here because of limitations [26] of their analytic procedures.Both orders of  D,NaL and  D,NaLPic essentially agreed with each other (see Table 2).These facts suggest that an interaction of the diluent molecules with NaL + Pic − is fundamentally similar to that with NaL + .Again, its main interaction with Bz molecules occurs around NaL + moiety of the ion-pair complex.

Conclusions
The compositions of the ion-pair complexes, NaLPic, extracted into the Bz phases were clarified again and their few dissociations were shown from the magnitudes of log  1,Bz values.The Δ eq values at the Bz/w interfaces were easily calculated from the experimentally obtained log  D,Pic values.Namely, the presence of Δ eq at a less-polar diluent/w interface was clarified, as well as those at the polar diluents/w interfaces.Also, log  ex± values for the NaPic extraction with L into Bz were proportional to the −Δ eq ones and the slope of its regression line was about 84 V −1 .The order of the slopes is NB < DCM ≤ DCE < Bz, although its meaning is not still clear.Besides, by comparing the actual  D,NaL with  D,NaLPic values, it was suggested that the main interaction site of Bz molecules with NaL + Pic − is NaL + moiety in their ion pairs.The authors hope that the present study will become a topic which connects the extraction chemistry with the electrochemistry at the o/w interfaces.

A. Check of the Employed Data by Benford's Law
As reference, Benford's law [27] was checked on data of 228 in Tables 1 and 2 and the text.These results were 49 frequencies (21%) for Figure 1, 52 (23%) for Figure 2, 51 (22%) for Figure 3, 19 (8.3%) for Figure 4, 10 (4.4%) for Figures 5 and 6, 9 (3.9 %) for Figure 7, 16 (7.0%)for Figure 8, and 12 (5.3%)for Figure 9. On the other hand, the theoretically calculated rates are 30% for Figure 1, 18% for Figure 2, 12% for Figure 3, 10% for Figure 4, 8% for Figure 5, 7% for Figure 6, 6% for Figure 7, and 5% for Figures 8 and 9 [27].Although the rate of Figure 1 (or Figure 3) was somewhat smaller (or larger) than the calculated rate of the corresponding figure, we can see that the law was roughly satisfied in our data determined and cited here.Consequently, the above analysis shows that the data are not being falsified knowingly.

B. Empirical Parameters Which Express L's Characteristics with Their Exchanges
For example, changing L from 15C5 to B15C5 simultaneously causes changes among their molecular volumes, the basicity of the donor oxygen atoms, and ring flexibilities of L. Namely, in the comparison between these Ls, the three parameters vary at least.Such conditions can hold on the comparisons between other Ls.So we classified the conditions for some Ls in the following table .Here, these figures in Table 3 are empirical values in many cases.Accordingly, only the relative order expressed by the figures is important for the discussion in the text (see Section 3.4).These orders were essentially based on data available in references: estimated cavity sizes [28] of L for , the molar volumes [12][13][14][15] for V, group electronegativities () of -OCH 3 ( = 2.68 [29]) and -OC 6 H 5 (2.65, evaluated here from the procedure in [25]) for B, ratio between the Na + radius [30] and the cavity size [28] of L for   , and the presence or absence of benzo groups for .
In addition to the above estimation based on the combined parameters, Table 3 can be employed as follows.Consider a comparison of L = 15C5 with 18C6.Comparing the rows of two Ls, one can see that changing from 15C5 to 18C6 means changes of the four parameters , , , and   at least.That is, one can understand immediately parameters which are changed by the exchange of L. Such comparisons with changes in some parameters make an explanation of differences in properties between Ls more difficult.However, we believe that such an idea is useful for considering the essence of the exchanges of L.

Figure 4 :
Figure 4: Plot of log  ex± versus −Δ eq for the NaPic extraction with L into Bz.See the text for the regression line.

3 ]
+ and  +  − into Bz.The following relation can be used for  D,NaL S evaluation: log  D,ML S = log  D,ML − Δ eq and the symbol  D,NaL S denotes the distribution constant,  D,NaL , of NaL + into the Bz phase at Δ eq = 0 V.As can be seen from Table2(see the values of footnote d and Appendix A for reference), log  D,NaL S values were in the orders DCE < DCM < NB < Bz for L = 15C5, DCE < DCM < Bz < NB for B15C5, NB < DCM < DCE < Bz for 18C6, and DCM < Bz < DCE < NB for B18C6.These orders indicate that the addition of the benzo group to the ring skeleton causes an increase in an interaction between NaL + and NB molecules.The larger  D,NaL S values for Bz systems (Table 2) do not necessarily show surprising results.Consider  D,NaL S value, using the thermodynamic relation, log  D,ML S = log  ex± + log( D,L / ML ) − log  D,A S .Here,  D,L and  ML refer to the 3 6 }.Similarly, log{ D,15C5 (Bz)/ D,15C5 (NB)} and − log{ D,Pic S (Bz)/  D,Pic S (NB)} were −0.15 {= −0.81 [12] − (−0.66 [18])} and +8.25 8 {= −(−8.208− 0.05 [20])}, respectively.Therefore, log { D,NaL S (Bz)/ D,NaL S (NB)} value becomes 2.8 3 .From such handling, we can see that the difference (= +8.26) in log  D,Pic

Table 1 :
Extraction data of the NaPic systems with L into Bz at 25 ∘ C. Values obtained from the analyses of the log  ex mix versus − log([Na + ][L] Bz ) plots.b See the text for the evaluation.c Values obtained from the analyses of the log  ex mix versus −(1/2) log  plots.d Mean values of ionic strength for the w or the Bz phase.
e Values calculated from the thermodynamic relation, log  1,Bz = log  ex a − log  ex± c .f Mean values calculated from the relation,  D,ML ≈  Bz  D,L / ML [M + ][L] Bz .g Mean values calculated from the relation, Δ ML 0 = Δ eq − 0.05916 log  D,ML at 25 ∘ C. h Mean values calculated from the relation,  ex± ≈  Bz 2 /.i Values calculated from the thermodynamic relation, log  D,ML = log  ex± + log( D,L / ML ) − log  D,A .j Values calculated from the values of footnote h for convenience, because the  ex± values of footnote c showed the larger calculation errors.

Table 1 .
Tendencies of the  , and  1, Values.The experimental log  D,Pic values of the Bz systems agreed with each other within experimental errors among L listed in At least, the values for L = 15C5 and 18C6 were much larger than log  D,Pic S one (= −8.208 [22] = Δ Pic 0 /0.05916 at 25 ∘ C) without L.This fact indicates that the presence of L, namely, the distribution of NaL + , in the extraction largely facilitates Pic − transfer at Bz/w interfaces.A plot of log( Bz /) (= ) versus log  D,Pic (= ) gave a straight line with a slope of 1.4 5 ±0.2 3 and an intercept of 1. 7 ± 1. 1 at  = 0.975.Although the slope value is larger than unity, this linear relation is similar to those reported before for the extraction systems of CdPic 2

Table 2 :
Individual distribution constants of NaL + and NaL + Pic − into some diluents at 25 ∘ C. Standard values calculated from the thermodynamic relation, log  D,ML S = log  ex± + log( D,L / ML ) − log  D,A S .Unpublished data by Kudo.d Standard values calculated from (5). e Values determined by ion-transfer polarographic measurements at the presence of 0.05 M (C 4 H 9 ) 4 N + B(C 6 H 5 ) 4 − in the NB phase.See [18].f Values determined by the ion-transfer polarographic measurements at the presence of 0.05 M (C 4 H 9 ) 4 N + B(C 6 H 5 ) 4 − in the NB phase.See [19].
a b See footnote f in Table 1.c g Not determined.h

Table 3 :
A measure of basic parameters for a comparison between Ls.